Under-pressure Culture Secretary Jeremy Hunt is braced for more revelations as his former special adviser and top civil servant give evidence to the Leveson Inquiry into media standards.

Labour has renewed calls for Mr Hunt to quit after the inquiry was shown a memo he sent to Prime Minister David Cameron arguing the case for News Corporation to take over BSkyB, just weeks before he was given quasi-judicial oversight of the bid.

The note warned that Business Secretary Vince Cable's decision to refer the bid to regulator Ofcom could leave the Government "on the wrong side of media policy".

More emails and text messages are expected to be published as the Culture Secretary's ex-special adviser, Adam Smith - who resigned after admitting getting too close to News Corp lobbyist Fred Michel - returns to give further evidence to the inquiry.

Also appearing before Lord Justice Leveson will be the senior civil servant at Mr Hunt's Department of Culture Media and Sport, Permanent Secretary Jonathan Stephens.

Mr Stephens was dragged into the row after Mr Hunt told MPs he had "approved" the nomination of Mr Smith as a point of contact with News Corp. The civil servant repeatedly refused to confirm or deny this during a subsequent appearance before a parliamentary committee, and later said in a letter only that he was "aware and content" with the arrangement.

In his memo to the Prime Minister, sent in November 2010, Mr Hunt warned that News Corp's James Murdoch was "pretty furious" over the Ofcom referral for the company's offer to buy the 61% share of the satellite broadcaster which it did not already own.

The Culture Secretary told Mr Cameron that News Corp's plan to create a multi-platform operation gave the UK "the chance to lead the way" on media globally. Without it, Britain's media sector would "suffer for years", and it would be "totally wrong to cave in" to opponents of the move.

Labour deputy leader Harriet Harman said: "It is clear... that David Cameron gave responsibility to Jeremy Hunt for deciding on the BSkyB bid when he knew only too well that the Culture Secretary was actively supporting the bid. The Prime Minister should never have given him the job. It is clear that Jeremy Hunt was not the impartial arbiter he was required to be, and he should already have resigned."

But Downing Street played down the memo's significance, pointing out that Mr Hunt had already made supportive comments about the bid in press interviews earlier that year. A Number 10 spokesman said: "Jeremy Hunt's note is entirely consistent with his public statements on the BSkyB bid prior to taking on the quasi-judicial role. It also makes clear that 'it would be totally wrong for the Government to get involved in a competition issue which has to be decided at arm's length'. The PM has made clear throughout that he recused himself from decisions relating to BSkyB and did not seek to influence the process in any way."